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  • 1. Chapter 2 Gases
  • 2. 12.1 Characteristics of Gases
    • Properties of Gases
      • because gas particles are far apart,
      • gases are fluids (they can flow)
      • gases have low density
      • gases are highly compressible
      • gases completely fill a container
  • 3. 12.1 Characteristics of Gases
    • Gas Pressure
      • Rene Descarte (1596-1650): rejected idea of void or vacuum
      • Pierre Gassendi (1592-1655): revived atomism; promoted idea of atoms moving in a void
      • Evangelista Torricelli (1608-1647): built a mercury barometer in 1643; created a vacuum
  • 4. Mercury Barometer
  • 5. 12.1 Characteristics of Gases
    • Gas Pressure
      • Blaise Pascal (1623-1662): tested atmospheric pressure at prompting of Descarte; found that pressure drops with altitude; believed in the vacuum
  • 6. 12.1 Characteristics of Gases
    • Gas Pressure
      • pressure is force divided by area
        • force: Newton (1 kg  m/s 2 = 1 N)
        • area: meter squared (m 2 )
        • pressure: Pascal (1 Pa = 1 N/1 m 2 )
      • for comparisons, standard temperature and pressure (STP): 0  C and 1 atm
  • 7. Pressure Units
  • 8. 12.1 Characteristics of Gases
    • Kinetic-Molecular Theory
      • gas particles are in constant, rapid, random motion
      • particles far apart relative to size
      • pressure due to collisions of particles with the walls of their container
  • 9. 12.1 Characteristics of Gases
    • Kinetic-Molecular Theory
      • gas temperature is proportional to average kinetic energy
        • gas molecules have a range of speeds
        • increasing temperature shifts the distribution
  • 10. Gas Molecules Energy Distribution
  • 11. 12.2 The Gas Laws
    • Measurable Properties of Gases
      • P = pressure exerted by gas
      • V = total volume occupied by gas
      • T = temperature in kelvins of gas
      • n = number of moles of gas
  • 12. 12.2 The Gas Laws
    • Robert Boyle (1627-1691): published The Spring of Air in 1660, which explained his most famous experiment
      • Boyle put mercury in a j-tube (manometer), and saw that when he doubled the pressure, the volume of air in short end halved
  • 13. Boyle’s Experiment
  • 14. Boyle’s Law
  • 15. 12.2 The Gas Laws
    • Robert Boyle
      • Boyle’s law:
        • PV = k
        • P 1 V 1 = P 2 V 2
  • 16. Boyle’s Law
  • 17. 12.2 The Gas Laws
    • Jacques Charles: discovered that a gas’s volume is proportional to temperature at constant pressure in 1787
      • Charles’s law:
        • V / T = k
        • V 1 / T 1 = V 2 / T 2
  • 18. Charles’s Law
  • 19. 12.2 The Gas Laws
    • Joseph Gay-Lussac (1778-1850): discovered in 1802 that increasing temperature at constant volume resulted in a proportional increase in pressure
      • Gay-Lussac’s law:
        • P = kT
        • P / T = k
        • P 1 / T 1 = P 2 / T 2
  • 20. Gay-Lussac’s Law
  • 21. 12.2 The Gas Laws
      • Gay-Lussac’s law of combining volumes (1809): gases combine in simple proportions by volume, and volume of products is related to volume of reactants
        • example 1: 2 volumes of H 2 react with 1 volume of O 2 to make 2 volumes of water
        • allowed Avogadro to deduce diatomic molecules (and more)
  • 22. Combining Volumes
  • 23. 12.2 The Gas Laws
    • Amadeo Avogadro (1776-1856): proposed in 1811 that equal volumes of all gases contain equal numbers of particles
      • Avogadro’s law:
        • V = kn
        • 1 mol of any gas at 0  C and 1 atm occupies 22.41 L
  • 24. Avogadro’s Law
  • 25. 12.2 The Gas Laws
    • Stanislao Cannizzaro (1826-1910): ~1858, deduced that Gay-Lussac’s law of combining volumes and Avogadro’s law could be used to calculate atomic and molecular weights relative to hydrogen; drew distinction between atoms and molecules; made a table of atomic weights
  • 26. Gas Laws Summary
  • 27. 12.3 Molecular Comp. of Gases
    • Ideal Gas Law
      • no gas perfectly obeys Boyle’s law, Charles’s law, Gay-Lussac’s law, or Avogadro’s law
      • although not perfect, these laws work well for most gases and most conditions
      • ideal gas : model gas that perfectly obeys gas laws
  • 28. Ideal Gases vs. Real Gases
  • 29. 12.3 Molecular Comp. of Gases
    • Ideal Gas Law
      • ideal gases
        • do not condense to liquids at low temperatures
        • do not have particles attracted to or repulsed by each other
        • have particles of no volume
        • do not exist
  • 30. 12.3 Molecular Comp. of Gases
    • Ideal Gas Law : combines four variables, P , V , T , and n , into one equation
      • PV = nRT
      • R is a proportionality constant
      • R = 8.314 L  kPa
      • mol  K
  • 31. 12.3 Molecular Comp. of Gases
    • Gas Behavior and Chemical Formulas
      • Diffusion : movement of particles from high concentration to low concentration
        • particles of lower mass diffuse more quickly than particles of higher mass
        • diffusion increases entropy
  • 32. 12.3 Molecular Comp. of Gases
    • Gas Behavior and Chemical Formulas
      • Effusion : passage of gas particles through a small opening
        • Graham’s law: rate of diffusion and effusion of a gas are inversely proportional to the square root of the gas’s density
  • 33. 12.3 Molecular Comp. of Gases
    • Gas Behavior and Chemical Formulas
        • Graham’s law, cont.
          • where v A and v B are molecular speeds of gases A and B and
          • M A and M B are the molar masses of gases A and B
  • 34. 12.3 Molecular Comp. of Gases
    • Gas Behavior and Chemical Formulas
        • Graham’s law, cont.
          • Graham’s law is easy to derive: solve the equation for the ratio of speeds between v A and v B
  • 35. 12.3 The Gas Laws
    • John Dalton (1766-1844): discovered that each gas in a mixture produces its own pressure as if it was alone
      • Dalton’s law of partial pressure: total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases
        • P total = P A + P B + P C